Wednesday, 4 November 2015

The distance to the Moon

I've recently been watching the wonderful HBO series From the Earth to the Moon, a dramatisation of NASA's Apollo missions to the Moon, which I'd highly recommend. As I've been watching it I've been reminded of some of the amazing contributions to science that these missions made. Its certainly true that their original motivation wasn't scientific, but that doesn't mean they didn't achieve anything scientifically.

One of their most important achievements is helping to precisely measure the distance to the Moon. Knowing the distance to the Moon and how this changes is important for understanding the orbit of the Moon, which influences tides on Earth, and whether the Moon is spiralling towards or away from the Earth.

Calculations from the ancient Greek astronomer
Aristarchus used to estimate the distance to the Moon
(Credit: Wikipedia)
Prior to the Apollo missions there were various methods to measure the distance to the Moon, including using radar and simple trigonometry. The ancient Greeks were the first to try to measure the distance to the Moon using trigonometry.

The astronomers Aristarchus and Hipparchus both succeeded in using this method, with the latter measuring a distance of about 410,000 km, an estimate which is only off by about 25,000 km, or 7% of the total distance.

To improve the distance measurements that were available at the time, the Apollo programme decided to take special reflectors to the Moon and leave them on the lunar surface. These specially-designed reflectors allow the distance between the Earth and the Moon to be measured by aiming lasers on Earth at the positions of these reflectors and then timing the amount of time it takes for the laser to be reflected back to Earth. Since we know how fast light moves through the vacuum of space we can use the time this journey takes to calculate the distance travelled.

The lunar ranging equipment, as left by Apollo 11 (Credit: NASA)

Once the reflectors were installed by Neil Armstrong and Buzz Aldrin of Apollo 11, a number of telescopes around the world were able to use them to measure the distance to the Moon. Additional reflectors were also left on the lunar surface by the Apollo 14 and 15 missions, with the latter using a particularly large reflector array that was three times the size of the other two reflectors. The majority of distances measurements to the Moon since then have used the Apollo 15 reflector due to its size.

Thanks to the precise measurements that these reflectors have allowed we have learnt a considerable amount about how the distance between the Earth and the Moon is changing. The distance to the Moon, which is approximately 385,000 km, is now known with an accuracy of better than one part in 10 billion. The exact distance changes throughout the Moon's orbit around the Earth, as well as due to a number of smaller effects.

One of those small effects is that the Moon is very slowly moving away from the Earth, at a rate of about 3.8 cm per year. While this is only a tiny fraction of the total distance between the Earth and the Moon it is surprisingly high! Don't worry though, at that rate it would take millions of years for there to be any perceptible change in the Moon's appearance from Earth!
Artist's rendering of the lunar core (Credit: NASA)

Variations in lunar rotation and orbit, measured thanks to these reflectors, have also provided evidence that the Moon probably has a liquid core. This core is thought to be about 20% of the Moon's radius. Seismographic measurements since then have refined this picture, suggesting that the Moon may have a solid inner core surrounded by a fluid and partially-fluid outer core.

Perhaps the most important use of knowing the precise distance to the Moon is the impact of the Moon on the rotation of the Earth, due to tidal gravitational forces. We now know, for example, that the Moon has a small effect on the length of the Earth day, which is changing very slowly due to this effect.

Nick Wirght (2015), The distance to the Moon (Blogger).

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